Simplify the expression. $(-t+1)(-3t+7)$
Solution: First distribute the ${-t+1}$ onto the ${-3t}$ and ${7}$ $ = {-3t}({-t+1}) + {7}({-t+1})$ Then distribute the ${-3t}.$ $ = ({-3t} \times {-t}) + ({-3t} \times {1}) + {7}({-t+1})$ $ = 3t^{2} - 3t + {7}({-t+1})$ Then distribute the ${7}$ $ = 3t^{2} - 3t + ({7} \times {-t}) + ({7} \times {1})$ $ = 3t^{2} - 3t - 7t + 7$ Finally, combine the $x$ terms. $ = 3t^{2} - 10t + 7$